Depending on whether the search engine in question allows it (I believe that google does) "Logical Not" might work. If that fails, negation may or may not work. It really depends on what you're trying to find out in a given situation and where your searches are being executed, as well as how the writers of a given site/paper used the term.

In mathematics, an inverse function is a function that undoes another function: If an input x into the function ƒ produces an output y, then putting y into the inverse function g produces the output x, and vice versa. i.e., ƒ(x)=y, and g(y)=x. More directly, g(ƒ(x))=x, meaning g(x) composed with ƒ(x) leaves x unchanged.A function ƒ that has an inverse is called invertible; the inverse function is then uniquely determined by ƒ and is denoted by ƒ−1 (read f inverse, not to be confused with exponentiation).

As such, a -1 is not necessarily the negation of 1, as it is not a boolean true/false statement. In programming, sometimes integer values are used in lieu of boolean values, but generally they are either part of an evaluation that returns a boolean result, like if(x >= y), or, when used to act as a boolean flag, the compiler (generally) only checks if the value is zero (0) for FALSE and any other value for TRUE.

IIRC Inverse just means the switching of positions of the head and tail. I.e, since (x == x/1) thus the inverse is therefore 1/x.

When talking about mathematics like this, it's best to talk in mathematics, i.e, provide examples instead of relying on pure literature.

I mean, the function is defined as "f(x) = -x", you can't define it any better than that. In words it'd be something like for every number x inserted into the function f you would get -x or something silly like that.

However, if you're worried that your readers will get confused by the use of 'Negation' or 'Inverse' in these cases, then you're probably focusing on the wrong thing. If you're still worried, select whichever word you like best, define it as succinctly as you can, then proceed to write the rest of your documentation and your language.

Is Multiplicative Inverse. Which is, honestly, the more 'usual' use of the term 'inverse' in mathematics. At least, I know that I've had math teachers correct me when I use x = - x to define 'inverse' as a general term. However, if you say 'inverse: x = -x' in a definition, I doubt that there would be much confusion, especially if there's any sort of context where it's used.

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